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Home / Doubts and Solutions/JEE/Mathematics

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Question no 22

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Asked by shobhit 6th October 2018, 4:31 PM
Answered by Expert
Answer:
begin mathsize 16px style open vertical bar straight z space plus space 1 over straight z close vertical bar equals space 2 rightwards double arrow open vertical bar straight z space plus space 1 over straight z close vertical bar squared equals space 4 rightwards double arrow open vertical bar straight z space plus space 1 over straight z close vertical bar open vertical bar straight z with bar on top space plus space fraction numerator 1 over denominator straight z with bar on top end fraction close vertical bar equals space 4 rightwards double arrow open vertical bar z close vertical bar squared space space plus space fraction numerator straight z over denominator straight z with bar on top end fraction space plus space space fraction numerator straight z with bar on top over denominator z end fraction plus space 1 over open vertical bar z close vertical bar squared space equals space 4 rightwards double arrow open vertical bar z close vertical bar squared space plus space 2 space Re space fraction numerator straight z over denominator straight z with bar on top end fraction space plus space 1 over open vertical bar straight z close vertical bar squared equals space 4 open parentheses Let space straight z space equals space straight x space plus space iy space space rightwards double arrow open vertical bar straight z close vertical bar space equals space straight x squared space plus space straight y squared close parentheses fraction numerator straight z over denominator straight z with bar on top end fraction space equals space fraction numerator straight x space plus space iy space over denominator straight x space minus space iy end fraction cross times fraction numerator straight x space plus space iy over denominator straight x space plus space iy end fraction space equals space fraction numerator straight x squared space minus space straight y squared space over denominator straight x squared space plus space straight y squared end fraction plus space fraction numerator 2 xyi over denominator straight x squared space plus space straight y squared end fraction rightwards double arrow open parentheses straight x squared space plus space straight y squared close parentheses space plus space 2 open parentheses fraction numerator straight x squared space minus space straight y squared space over denominator straight x squared space plus space straight y squared end fraction close parentheses space plus space fraction numerator 1 over denominator open parentheses straight x squared space plus space straight y squared close parentheses end fraction equals space 4 rightwards double arrow open parentheses straight x squared space plus space straight y squared close parentheses squared space plus space 2 open parentheses straight x squared space minus space straight y squared close parentheses space plus space 1 equals space 4 open parentheses straight x squared space plus space straight y squared close parentheses rightwards double arrow open parentheses straight x squared space plus space straight y squared close parentheses squared space minus 4 open parentheses straight x squared space plus space straight y squared close parentheses space plus space 1 space plus 2 open parentheses straight x squared space minus space straight y squared close parentheses equals space 0 rightwards double arrow open parentheses straight x squared space plus space straight y squared close parentheses squared space minus 2 straight x squared space minus space 2 straight y squared space minus 4 straight y squared space plus space 1 equals space 0 rightwards double arrow open parentheses straight x squared space plus space straight y squared close parentheses squared space minus space 2 open parentheses straight x squared space plus space straight y squared close parentheses space plus space 1 space minus space 4 straight y squared space equals space 0 rightwards double arrow open parentheses straight x squared space plus space straight y squared minus space 1 close parentheses squared minus space open parentheses 2 straight y close parentheses squared space equals space 0 rightwards double arrow open parentheses straight x squared space plus space straight y squared minus space 1 space minus 2 straight y close parentheses open parentheses straight x squared space plus space straight y squared minus space 1 space plus 2 straight y close parentheses equals space 0 rightwards double arrow open parentheses straight x squared space plus space straight y squared minus 2 straight y space plus 1 space minus 1 space minus 1 close parentheses open parentheses straight x squared space plus space straight y squared space plus space 2 straight y space plus space 1 space minus 1 space minus 1 close parentheses equals space 0 rightwards double arrow open square brackets straight x squared plus space open parentheses straight y space minus space 1 close parentheses squared minus space 2 close square brackets open square brackets straight x squared plus space open parentheses straight y space plus space 1 close parentheses squared minus space 2 close square brackets equals space 0 rightwards double arrow straight x squared plus space open parentheses straight y space minus space 1 close parentheses squared space equals space 2 space space or space straight x squared plus space open parentheses straight y space plus space 1 close parentheses squared space space equals space 2 We space use space open vertical bar straight z close vertical bar squared space equals space straight z. stack space straight z with bar on top and space finally space we space get space circles space having space centres space left parenthesis 0 comma space 1 right parenthesis space and space left parenthesis 0 comma space minus 1 right parenthesis space having space radius space square root of 2 unit space. Two space circles space are space congruent space if space they space have space same space diameter. Ans colon space Option space left parenthesis straight C right parenthesis end style
Answered by Expert 18th October 2018, 3:53 PM
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